Cameras are commonly used to capture an image of a scene that includes one or more objects. Unfortunately, some of the images are blurred. For example, movement of the camera and/or movement of the objects in the scene during the exposure time of the camera can cause the image to be blurred. Further, if the camera is not properly focused when the image is captured, the image can be blurred.
When blur is sufficiently spatially uniform, a blurred captured image can be modeled as the convolution of a latent sharp image with some point spread function (“PSF”) plus noise,B=K*L+N.  Equation (1)
In Equation 1 and elsewhere in this document, (i) “B” represents a blurry image, (ii) “L” represents a latent sharp image, (iii) “K” represents a PSF kernel, and (iv) “N” represents noise (including quantization errors, compression artifacts, etc.). A blind deconvolution problem seeks to recover both the PSF kernel K and the latent sharp image L. The blind deconvolution problem is often very difficult to accurately solve.
One common approach to solving a deconvolution problem includes reformulating it as an optimization problem in which suitable cost functions are minimized in order to find a solution to the deconvolution problem. For example, the blind deconvolution problem is often solved in iterations by minimizing two cost functions in alternating fashion. More specifically, the blind deconvolution problem is often solved in iterations by minimizing a latent sharp image estimation cost function, and by minimizing a PSF estimation cost function in alternating fashion.
A relatively common type of a cost function used for deconvolution is a regularized least squares cost function. Typically, a regularized least squares cost function consists of (i) one or more fidelity terms, which make the minimum conform to equation (1) modeling of the blurring process, and (ii) one or more regularization terms, which make the solution more stable and help to enforce prior information about the solution, such as sparseness.
One example of a PSF estimation cost function is provided in below in Equation 2:c(K)=∥Lx*K−Bx∥2+∥Ly*K−By∥2+θ∥K∥2+σ(∥Kx∥2+∥Ky∥2).  Equation (2).
In Equation 2, c(K) is the PSF estimation cost function, K denotes the PSF kernel that is to be estimated, B is a given blurry image, L is an estimate of the latent sharp image, θ and σ are regularization term weights, and subscripts x and y denote derivatives in x- and y-direction. If the convolution operator * is assumed to be periodic, the minimum of the PSF cost function in Equation 2 can be found very quickly, by evaluating a closed form formula for the minimum in the Fourier domain, and the Fast Fourier Transform can be used for an efficient implementation.
Unfortunately, many blurry images include areas that complicate the problem of accurately determining the PSF kernel. For example, when the blurry image contains more strong edges in some directions than in others, the estimated PSF kernel tends to be inaccurate. More specifically, when strong straight edges are present in the blurry image, the PSF kernel estimated by minimizing the PSF cost function in Equation 2 tends to contain strong artifacts having the form of streaks along the dominant edge direction. Thus, existing regularized least squares cost functions are not entirely satisfactory.